Lax Representation and Darboux Solutions of the Classical Painlevé Second Equation | Zendy

Irfan Mahmood | Zendy; Muhammad Waseem | Zendy

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Lax Representation and Darboux Solutions of the Classical Painlevé Second Equation

Author(s) -

Irfan Mahmood,

Muhammad Waseem

Publication year - 2021

Publication title -

advances in mathematical physics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.283

H-Index - 23

eISSN - 1687-9139

pISSN - 1687-9120

DOI - 10.1155/2021/8851043

Subject(s) - integrable system , lax pair , mathematics , darboux integral , transformation (genetics) , representation (politics) , scheme (mathematics) , pure mathematics , algebra over a field , gauge (firearms) , mathematical physics , mathematical analysis , law , geometry , history , biochemistry , chemistry , archaeology , curvature , politics , political science , gene

In this article, we present Darboux solutions of the classical Painlevé second equation. We reexpress the classical Painlevé second Lax pair in new setting introducing gauge transformations to yield its Darboux expression in additive form. The new linear system of that equation carries similar structure as other integrable systems possess in the AKNS scheme. Finally, we generalize the Darboux transformation of the classical Painlevé second equation to the N -th form in terms of Wranskian.

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